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In this paper we resume the study of projective modules over semilocal rings we began in [12]. If R is a semilocal ring, the canonical projection T of R onto the semisimple artinian ring R/J (R) induces a semigroup homomorphism Sæ (T): S. 5 (P-Mod R)–SB (P-Mod R/J (R)), where SE (P-Mod S) denotes the semigroup of isomorphism classes of finitely generated projective modules over the ring S; this mapping St.(T) turns out to be a full affine embedding of the semigroup Se (P-Mod R) into the free commutative semigroup S4 (P-Mod R/J (R)). The main result of our paper [12] says that ev-ery full affine embedding of a semigroup M into a free commutative semigroup N” can be realized as the mapping Sq,(T): Sp (P-Mod R)—Sab (P-Mod R/J (R)) for a suitable (hereditary) semilocal ring R. More precisely, let k be a field, let M be a semigroup and let T: M→ N” be a full affine embedding. Assume that u e M is such that T (u)=(d1,..., dm) with di,..., d,# 0. Then there exists a semilo-cal hereditary k-algebra R such that the diagram of commutative semigroups and semigroup homomorphisms